Space of modular forms of level 91, weight 12, and trivial character

• Label: 91.12.a
• Level: $91$
• Weight: $12$
• Character orbit: 91.a
• Rep. character: $\chi_{91}(1,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(91))\).

	Total	New	Old
Modular forms	106	66	40
Cusp forms	102	66	36
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(-\)	$-$	\(15\)
\(-\)	\(+\)	$-$	\(16\)
\(-\)	\(-\)	$+$	\(18\)
Plus space		\(+\)	\(35\)
Minus space		\(-\)	\(31\)

Trace form

\( 66 q + 18 q^{2} + 40 q^{3} + 56590 q^{4} - 3916 q^{5} + 19496 q^{6} + 33614 q^{7} + 214686 q^{8} + 3207698 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(91))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	13
91.12.a.a	$91$	$12$	91.a	1.a	$1$	$15$	$15$	$69.919$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-77\)	\(10\)	\(-13522\)	\(-252105\)		$+$	$-$	$-$	$2^{16}\cdot 3^{6}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q+(-5-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
91.12.a.b	$91$	$12$	91.a	1.a	$1$	$16$	$16$	$69.919$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-10\)	\(-476\)	\(-19686\)	\(268912\)		$-$	$+$	$-$	$2^{16}\cdot 3^{6}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-30-\beta _{3})q^{3}+(479+\cdots)q^{4}+\cdots\)
91.12.a.c	$91$	$12$	91.a	1.a	$1$	$17$	$17$	$69.919$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(19\)	\(-476\)	\(8551\)	\(-285719\)		$+$	$+$	$+$	$2^{18}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(-28-\beta _{1}-\beta _{3})q^{3}+\cdots\)
91.12.a.d	$91$	$12$	91.a	1.a	$1$	$18$	$18$	$69.919$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(86\)	\(982\)	\(20741\)	\(302526\)		$-$	$-$	$+$	$2^{18}\cdot 3^{5}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q+(5-\beta _{1})q^{2}+(55-\beta _{1}+\beta _{3})q^{3}+(35^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(91))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(91)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)